In each of the following figure, find the value of x:

Δ ABC is isosceles with AB = AC

∠BAC = 40⁰(Given)

In an isosceles triangle since the base angles are equal so

∠ABC = ∠ACB = y (Let’s assume)

∠ABC + ∠ACB + ∠BAC = 180⁰(Sum of interior angles of a triangle)

⇒ 2y = 180⁰-40⁰ = 140⁰

⇒ y = 70⁰

⇒ ∠ACB = 70⁰

∠ACB + x = 180⁰(Angle on a straight line)

⇒ x = 180⁰ - 70⁰ = 110⁰